积分的下极限

Both of them are the normal distance of the tangent plane at the check point on the limit state surface in the generalized stochastic space and the asymptotic formula for Laplace''s integral respectively.

提出了利用广义随机变量空间失效极限状态曲面上验算点处切平面法线和Laplace型积分渐近公式两种确定任意分布的荷载变量相关下结构的可靠指标的新方法，改进了现行防波堤失效概率计算理论。

Utilizing the tools of conformal mapping and Cauchy integral formula and so on, the SIFs at the crack tips are obtained, which can be reduced to the known results under the condition of limitation; For the third and the fourth section, the problems of arc crack and parabolic crack are researched in one dimensional hexagonal QCs.

第二节研究了一维六方准晶狭长体中双半无限共线裂纹问题，利用保角变换以及Cauchy积分公式等工具求得了裂尖处的应力强度因子，在极限的情况下可以还原为若干已有的结果。

The asymptotic property of the modified supremum-type statistic and the integral-type statistic under the composite null hypothesis are derived.

对上界型检验统计量，研究了与之有关的一个极限性质；对积分型检验统计量，证明了其在复合零假设下的渐近分布。

Integral of one variable functions, improper integral and its convergence properties.

本课程的主要内容包括：1 各种极限运算，其中包括数列极限、函数极限以及上、下极限；2 一元函数的微分学，包括微分和导数的运算法则、微分中值定理及其应用等；3 一元函数的积分和广义积分及其收敛性；4 级数及其收敛性，包括数值级数的收敛性和函数项级数的各种运算和性质；5 多元函数的微分学及其应用，其中很多方面与一元函数的微分学近似，需要注意它们之间的区别；6 多元函数的积分学，包括多重积分的性质与计算，多重积分的的应用等；7 曲线、曲面积分及其应用；8 含参变量积分的计算与性质；9 Fourier 级数及其应用，等等。

In this paper we have obtained the sufficient and necessary condition concerning the passage to the limit under the integral sign, and have given some examples of the problems which can be solved by the theorem of this paper but cannot be solved by the familiar Vitali's theorem.

关于积分号下取极限的问题，有著名的Lebesgue定理及Vitali定理。本文作者进一步研究了这一问题，得到了积分号下取极限的充分和必要条件，并给出了几个能用本文结果解决而不能用Vitali定理解决的例子。

There are proved the theorems on convergence of sequences of the integral, which are similar to Levi's theorem, Fatou's theorem and so on in Lebesgue's integral.

4中引进了一类特殊的所谓λ次可加模糊测度空间，给出了这种测度空间上收敛性的Егоров定理和Riesz定理并得到了该空间上的模糊积分在积分号下取极限的一些充分条件。

Limit theorems for the integration of function sequence with respect to weak convergence probability measure sequence are proved under the condition of the weak tight, which have been used to research the some convergence of expectant functional sequence,and a sufficient condition for the epi-convergence of expectant functional sequence is obtained.

提出了弱胎紧的概念，并在弱胎紧的条件下证明了函数序列关于弱收敛概率测度序列积分的极限定理，用其研究了期望泛函序列的若干收敛性，得到了期望泛函序列的、上图收敛的一个充分条件。

The probability limit theorem is used to design a kind of Monte Carlo method of dual integral.

利用概率极限定理思想，设计二重积分的蒙特卡罗算法，通过方差分析，选择适当的随机数，得到了理论意义下的方差最小算法，用实际算例验证了该方法的优良性。

Under the limiting constrained conditions, an attempt to improve ship hull form of minimized wavemaking resistance is described by taking improved Michell integration as an object function and UV as an optimized design variable that is a mapping transformation function for the harmonizing and the fairing of the form variation.

在极限约束条件下，基于船体型值与UV度的映射函数，用UV度作为优化设计变量，以改进的Michel积分为目标函数，求得具有很好的协调性和工程光顺性的最小兴波阻力船型。

The expression of the complex equipment failure rate under the normal operating conditions were researched based on the renewal theory .

基于更新理论，研究了正常使用条件下复杂设备故障率λ的表达问题，结果表明：对任意的故障分布，复杂设备故障率λ的极限为一积分表达式，仅在指数分布时，该极限是一个常数。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。